Links: [ University | Computer Science and Software Engineering ] Concordia University home page

Bart Oldeman

Research Associate

Contents: [ Contact Details | Research and Publications | Teaching | Links ]

Contact Details

Department of Computer Science and Software Engineering,
Concordia University,
1455 De Maisonneuve Blvd. West,
Montreal, Quebec, H3G 1M8
Canada

Telephone: +1 514 848 2424 ext 7953
E-mail: boldeman at encs dot concordia dot ca

Research and Publications


In January 2007 I started a position as a research associate with Eusebius Doedel. I am working on the software AUTO-07P, improving its parallellization capabilities, and making the Python interface that was originally written by Randy Paffenroth more capable, so we can easily extract data and paste together calculations, that so far required a lot of manual intervention and ad-hoc scripts.
We are also using this tool, in particular investigating manifolds and global bifurcation, such as homoclinic and heteroclinic connections. We collaborate with people at McGill's Center for Nonlinear Dynamics such as Leon Glass and Michael Guevara, and in the past I looked at a model for travelling waves of calcium in pancreatic acinar cells by James Sneyd
Another project is to automatically be able to find codimension-one bifurcations directly from codimension-two bifurcation points
Previously, in June 2004 I started a two year postdoctoral research fellowship with Vivien Kirk. and I was working with Alan Champneys and Bernd Krauskopf at the University of Bristol on a dynamical-systems analysis of a new class of global bifurcations: local codimension-two bifurcations in the presence of a global reinjection mechanism. The main example is a saddle-node Hopf (SNH) bifurcation at an equilibrium on a limit cycle.
This bifurcation is an organising centre for the dynamics of a semiconductor laser with optical reinjection. I used both analytical and numerical techniques to study this bifurcation.
In my PhD project I have developed a technique for homoclinic branch switching for this software, which was incorporated in the main version.
Moreover, in the second half of 2002 I was working with Björn Sandstede at Ohio State University to refine the homoclinic branch switching methods and work on the numerical continuation of defects.

Publications

  • A. R. Champneys, V. Kirk, E. Knobloch, B. E. Oldeman, and J. D. M. Rademacher, ``Unfolding a tangent equilibrium-to-periodic heteroclinic cycle'', SIAM J. Appl. Dyn. Syst., 8 (2009) 1261-1304.
  • H. G. E. Meijer, F. Dercole, and B. E. Oldeman, ``Numerical Bifurcation Analysis'', in R. A. Meyers (Ed.), in Encyclopedia of Complexity and Systems Science, Springer (2009) 6329-6352.
  • A. R. Champneys, V. Kirk, E. Knobloch, B. E. Oldeman, and J. Sneyd, ``When Shil'nikov meets Hopf in excitable systems'', SIAM J. Appl. Dyn. Syst., 6 (2007) 663-693.
  • B. Krauskopf and B. E. Oldeman, ``Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation'', Nonlinearity 19(9) (2006) 2149-2167.
  • B. Krauskopf and B.E Oldeman ``A planar model system for the saddle-node Hopf bifurcation with global reinjection'', Nonlinearity 17(4) (2004) 1119-1152
  • B. E. Oldeman, A. R. Champneys and B. Krauskopf, ``Homoclinic branch switching: a numerical implementation of Lin's method'', Int. J. of Bifurcation and Chaos 13(10) (2003) 2977-2999
  • B. E. Oldeman, B. Krauskopf and A. R. Champneys, ``Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations'', Nonlinearity 14(3) (2001) 597-621
  • B. E. Oldeman, B. Krauskopf and A. R. Champneys, ``Death of period-doublings: locating the homoclinic-doubling cascade'', Physica D, 146(1-4) (2000) 100-120

    Proceedings Contributions

  • B. E. Oldeman and B. Krauskopf, ``A vector field model of a saddle-node Hopf bifurcation with global reinjection'', in Proceedings of Equadiff 2003, World Scientific (2005), 1114-1116.
  • B. Krauskopf, B. E. Oldeman and A. R. Champneys, ``Resonant homoclinic flip bifurcations: a numerical investigation'', in B. Fiedler, K. Gröger and J. Sprekels (Eds.), Equadiff 99, World Scientific (2000) 55-57

    Preprints

  • E. J. Doedel, B. E. Oldeman, and C. L. Pando. L., ``Bifurcation structures in a model of the CO2 laser with a fast saturable absorber'', submitted to Int. J. of Bifurcation and Chaos (2010).
  • F. Bizzarri, D. Linaro, B. Oldeman, and M. Storace, ``Harmonic analysis of oscillators through standard numerical continuation tools'', accepted by Int. J. of Bifurcation and Chaos (2010).
  • B. E. Oldeman, B. Krauskopf and A. R. Champneys, ``Numerical investigation of resonant homoclinic flip bifurcations I: The single homoclinic-doubling case'', Applied Nonlinear Mathematics Research Report 99.10, University of Bristol (1999)


    • Phd-project:

    PhD thesis:

     Numerical bifurcation analysis of multi-pulse homoclinic orbits.  

    Numerical investigation of homoclinic doubling cascades

    Master's thesis:

     Analysis of Resonances in the Three Body Problem using Planar Reduction (gzipped postscript)

    Back to top